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George Pirlea
Iris
Commits
56321b0f
Commit
56321b0f
authored
Jun 13, 2017
by
Robbert Krebbers
Browse files
Remove `⌜φ⌝ ⊢ □ ⌜φ⌝` as a primitive rule, it can be derived.
parent
381e8509
Changes
2
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Side-by-side
theories/base_logic/derived.v
View file @
56321b0f
...
...
@@ -483,7 +483,12 @@ Lemma always_idemp P : □ □ P ⊣⊢ □ P.
Proof
.
apply
(
anti_symm
_
)
;
auto
using
always_idemp_2
.
Qed
.
Lemma
always_pure
φ
:
□
⌜φ⌝
⊣
⊢
⌜φ⌝
.
Proof
.
apply
(
anti_symm
_
)
;
auto
using
always_pure_2
.
Qed
.
Proof
.
apply
(
anti_symm
_
)
;
auto
.
apply
pure_elim'
=>
H
φ
.
trans
(
∀
x
:
False
,
□
True
:
uPred
M
)%
I
;
[
by
apply
forall_intro
|].
rewrite
always_forall_2
.
auto
using
always_mono
,
pure_intro
.
Qed
.
Lemma
always_forall
{
A
}
(
Ψ
:
A
→
uPred
M
)
:
(
□
∀
a
,
Ψ
a
)
⊣
⊢
(
∀
a
,
□
Ψ
a
).
Proof
.
apply
(
anti_symm
_
)
;
auto
using
always_forall_2
.
...
...
theories/base_logic/primitive.v
View file @
56321b0f
...
...
@@ -430,8 +430,6 @@ Qed.
Lemma
always_idemp_2
P
:
□
P
⊢
□
□
P
.
Proof
.
unseal
;
split
=>
n
x
??
/=.
by
rewrite
cmra_core_idemp
.
Qed
.
Lemma
always_pure_2
φ
:
⌜φ⌝
⊢
□
⌜φ⌝
.
Proof
.
by
unseal
.
Qed
.
Lemma
always_forall_2
{
A
}
(
Ψ
:
A
→
uPred
M
)
:
(
∀
a
,
□
Ψ
a
)
⊢
(
□
∀
a
,
Ψ
a
).
Proof
.
by
unseal
.
Qed
.
Lemma
always_exist_1
{
A
}
(
Ψ
:
A
→
uPred
M
)
:
(
□
∃
a
,
Ψ
a
)
⊢
(
∃
a
,
□
Ψ
a
).
...
...
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